Question

Let the length, breadth and height of the cuboid be l units, b units and h units respectively. Given, area of three adjacent faces of the cuboid are: $120c{m}^2;72c{m}^2;60c{m}^2$

Answer 1

Area of the face ABEF =$l\times b=120....\left(1\right)$
Area of the face ABCD = $l\times h=72...\left(2\right)$
Area of the face ADGF =$b\times h=60...\left(3\right)$
Multiplying (1), (2) and (3), we get
$(l\times b)\times (l\times h)\times (b\times h)=518400\therefore l^2{b}^2{h}^2=518400...\left(4\right)$
Volume of the cuboid =$l\times b\times h$
$\therefore V=lbh$
Squaring on both sides, we get
$V^2=l^2{b}^2{h}^2\therefore V^2=518400$
Taking square root both sides,
so, $V=720c{m}^3$